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What is the Least Common Multiple of 3670 and 3688?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 3670 and 3688 is 6767480.

LCM(3670,3688) = 6767480

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Least Common Multiple of 3670 and 3688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3670 and 3688, than apply into the LCM equation.

GCF(3670,3688) = 2
LCM(3670,3688) = ( 3670 × 3688) / 2
LCM(3670,3688) = 13534960 / 2
LCM(3670,3688) = 6767480

Least Common Multiple (LCM) of 3670 and 3688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3670 and 3688. First we will calculate the prime factors of 3670 and 3688.

Prime Factorization of 3670

Prime factors of 3670 are 2, 5, 367. Prime factorization of 3670 in exponential form is:

3670 = 21 × 51 × 3671

Prime Factorization of 3688

Prime factors of 3688 are 2, 461. Prime factorization of 3688 in exponential form is:

3688 = 23 × 4611

Now multiplying the highest exponent prime factors to calculate the LCM of 3670 and 3688.

LCM(3670,3688) = 23 × 51 × 3671 × 4611
LCM(3670,3688) = 6767480